Circuit-level design principles for transmission-mode microwave impedance microscopy

A recently developed technique of transmission-mode microwave impedance microscopy (T-MIM) has greatly extended the capabilities of standard reflection-mode MIM to novel applications, such as the in operando study of nanoscale electro-acoustic devices. As is common for new techniques, systematic design principles for boosting sensitivity and balancing bandwidth are lacking. Here, we show numerically and analytically that the T-MIM signal is proportional to the reflection-mode voltage enhancement factor ? of the circuit, as long as the output impedance of the local voltage source is properly treated. We show that this proportionality holds in the currently achievable "weak sampling" regime and beyond, for which we demonstrate a realistic path with commercially available superconducting components and critically coupled impedance matching networks. We demonstrate that for these next-generation designs, the sensitivity is generally maximized at a slightly different frequency from the unloaded S-11 resonance, which can be explained by the maximum power transfer theorem.